Bayesian network-based missing mechanism identification (BN-MMI) method in medical research

Focus of presentation Missing data are ubiquitous in medical research. Although there is increasing guidance on how to handle missing data, practice is changing slowly and misapprehensions abound, particularly in observational research. We present a practical framework for handling and reporting the analysis of incomplete data in observational studies, which we illustrate using a case study from the Avon Longitudinal Study of Parents and Children. Findings The framework consists of three steps: 1) Develop an analysis plan specifying the analysis model and how missing data are going to be addressed. Important considerations are whether a complete records analysis is likely to be valid, whether multiple imputation or an alternative approach is likely to offer benefits, and whether a sensitivity analysis regarding the missingness mechanism is required. 2) Explore the data, checking the methods outlined in the analysis plan are appropriate, and conduct the pre-planned analysis. 3) Report the results, including a description of the missing data, details on how missing data were addressed, and the results from all analyses, interpreted in light of the missing data and clinical relevance. Conclusions/Implications This framework encourages researchers to think carefully about their missing data and be transparent about the potential effect on the study results. This will increase confidence in the reliability and reproducibility of results from published papers. Key messages Researchers need to develop a plan for missing data prior to conducting their analysis, and be transparent about how they handled the missing data and its potential effect when reporting their results.

We illustrate a class of conditional models for the analysis of longitudinal data suffering attrition in random effects models framework, where the subject-specific random effects are assumed to be discrete and to follow a time-dependent latent process. The latent process accounts for unobserved heterogeneity and correlation between individuals in a dynamic fashion, and for dependence between the observed process and the missing data mechanism. Of particular interest is the case where the missing mechanism is non-ignorable. To deal with the topic we introduce a conditional to dropout model. A shape change in the random effects distribution is considered by directly modeling the effect of the missing data process on the evolution of the latent structure. To estimate the resulting model, we rely on the conditional maximum likelihood approach and for this aim we outline an EM algorithm. The proposal is illustrated via simulations and then applied on a dataset concerning skin cancers. Comparisons with other well-established methods are provided as well.

In biomedical research with longitudinal designs, missing values due to intermittent non-response or premature withdrawal are usually 'non-ignorable' in the sense that unobserved values are related to the patterns of missingness. By drawing the framework of a shared-parameter mechanism, the process yielding the repeated count measures and the process yielding missing values can be modelled separately, conditionally on a group of shared parameters. For chronic diseases, Markov transition models can be used to study the transitional features of the pathologic processes. In this paper, Markov Chain Monte Carlo algorithms are developed to fit a random-effects Markov transition model for incomplete count repeated measures, within which random effects are shared by the counting process and the missing-data mechanism. Assuming a Poisson distribution for the count measures, the transition probabilities are estimated using a Poisson regression model. The missingness mechanism is modelled with a multinomial-logit regression to calculate the transition probabilities of the missingness indicators. The method is demonstrated using both simulated data sets and a practical data set from a smoking cessation clinical trial.

A review on missing values for main challenges and methods

Missing data are uncollected data but meaningful for the statistical analysis due to clinical relevancy of the data for properly specified estimands in clinical trials. Meanwhile the efforts to prevent or minimize missing data are commonly applied in clinical trials, in practice, missing data still occurs. Choosing a statistical method for imputation that deals with missing data targeting specified estimands provides the more reliable estimates of treatment effects. We considered longitudinal clinical settings that have different degrees of missing data and treatment effects, and simulated different missing mechanisms using data from randomized, double-blind, placebo-controlled phase 3 confirmatory clinical trials of approved drugs. We compared four commonly used statistical methods to deal with missing data in clinical trials. We find that, when the data are missing not at random (MNAR) with higher missing rates, mixed model for repeated measurements (MMRM) method overestimates treatment difference. Pattern-mixture model estimates were seen to be more conservative in our studies than MMRM given MNAR assumptions, which are more realistic with missing datain clinical trials. We emphasize the importance of prevention of missing data and specifying the estimand based on trial objectives beforehand. The specified proper estimand and the proper statistical method might be key features to value the clinical trial results despite missing data.

Objective To explore the optimal fitting path of missing data of the Scale to make the fitting data close to the real situation of patients' data. Methods Based on the complete data set of the SDS of 507 patients with stroke, the data simulation sets of Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) were constructed by R software, respectively, with missing rates of 5%, 10%, 15%, 20%, 25%, 30%, 35%, and 40% under three missing mechanisms. Mean substitution (MS), random forest regression (RFR), and predictive mean matching (PMM) were used to fit the data. Root mean square error (RMSE), the width of 95% confidence intervals (95% CI), and Spearman correlation coefficient (SCC) were used to evaluate the fitting effect and determine the optimal fitting path. Results when dealing with the problem of missing data in scales, the optimal fitting path is ① under the MCAR deletion mechanism, when the deletion proportion is less than 20%, the MS method is the most convenient; when the missing ratio is greater than 20%, RFR algorithm is the best fitting method. ② Under the Mar mechanism, when the deletion ratio is less than 35%, the MS method is the most convenient. When the deletion ratio is greater than 35%, RFR has a better correlation. ③ Under the mechanism of MNAR, RFR is the best data fitting method, especially when the missing proportion is greater than 30%. In reality, when the deletion ratio is small, the complete case deletion method is the most commonly used, but the RFR algorithm can greatly expand the application scope of samples and save the cost of clinical research when the deletion ratio is less than 30%. The best way to deal with data missing should be based on the missing mechanism and proportion of actual data, and choose the best method between the statistical analysis ability of the research team, the effectiveness of the method, and the understanding of readers.

Longitudinal studies collect information on a sample of individuals which is followed over time to analyze the effects of individual and time-dependent characteristics on the observed response. These studies often suffer from attrition: individuals drop out of the study before its completion time and thus present incomplete data records. When the missing mechanism, once conditioned on other (observed) variables, does not depend on current (eventually unobserved) values of the response variable, the dropout mechanism is known to be ignorable. We propose a selection model extending semiparametric variance component models for longitudinal binary responses to allow for dependence between the missing data mechanism and the primary response process. The model is applied to a data set from a methadone maintenance treatment programme held in Sidney, 1986.

Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR. A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The implementation of the score tests circumvents the identification issue as it requires only parameter estimation under the null MAR assumption. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well-controlled type I errors and desirable powers.

Comparing Methods for Handling Missing Data

Missing data (MD) is a common and inevitable problem facing data mining (DM)-based decision systems in e-health since many medical historical datasets contain a huge number of missing values. Therefore, a pre-processing stage is usually required to deal with missing values before building any DM-based decision system. The purpose of this paper is to evaluate the impact of MD techniques on classification systems in cardiovascular dysautonomias diagnosis. We analyzed and compared the accuracy rates of four classification techniques: random forest (RF), support vector machines (SVM), C4.5 decision tree, and Naive Bayes (NB), using two MD techniques: deletion or imputation with k-nearest neighbors (KNN). A total of 216 experiments were therefore carried out using three missingness mechanisms (MCAR: missing completely at random, MAR: missing at random and NMAR: not missing at random), two MD techniques (deletion and KNN imputation), nine MD percentages from 10 to 90% over a dataset collected from the autonomic nervous system (ANS) unit of the University Hospital Avicenne in Morocco. The results obtained suggest that using KNN imputation rather than deletion enhances the accuracy rates of the four classifiers. Moreover, the MD percentages have a negative impact on the performance of classification techniques regardless of the MD mechanisms and MD techniques used. In fact, the accuracy rates of the four classifiers decrease as the MD percentage increases. Graphical abstract.

We aimed to investigate the association between body mass index (BMI) at the time of intensive care unit (ICU) admission and 90-day mortality risk in complete-case datasets that ignore missing data as well as in datasets with multiple imputation for missing data. This retrospective study analysed the medical records of adult patients admitted to ICUs in a single tertiary academic hospital. For BMI analysis, data were classified into four groups: underweight (<20 kg/m2 ), normal (20-24.9 kg/m2 ), overweight (25-29.9 kg/m2 ), and obese (≥30 kg/m2 ). A total of 24,928 patients were examined. Among them, 5,916 (23.7%) patients had missing BMI data at ICU admission, and the missing mechanism was not missing completely at random. In the multivariable Cox regression analysis, the 90-day mortality risk of underweight patients in the complete-case group increased by 1.49 times compared with that of normal BMI patients with a hazard ratio (HR) of 1.49 (95% confidence interval: 1.34-1.66; P<0.001), whereas the 90-day mortality risk of underweight patients in the multiple imputation group increased by 1.36 times compared with that of normal BMI patients (HR: 1.36, 95% confidence interval: 1.24-1.49; P<0.001). We showed that the occurrence of missing BMI data at ICU admission could affect the prediction of 90-day mortality in critically ill patients. Particularly, missing BMI data had the potential to slightly overestimate the 90-day mortality of underweight patients. Therefore, multiple imputation for missing BMI data can be an appropriate statistical option to reduce bias.

Imputation of missing values in residential building monitored data: Energy consumption, behavior, and environment information

Propensity score analysis is a popular method to control for confounding in observational studies. A challenge in propensity methods is missing values in confounders. Several strategies for handling missing values exist, but guidance in choosing the best method is needed. In this simulation study, we compared four strategies of handling missing covariate values in propensity matching and propensity weighting. These methods include: complete case analysis, missing indicator method, multiple imputation and combining multiple imputation and missing indicator method. Concurrently, we aimed to provide guidance in choosing the optimal strategy. Simulated scenarios varied regarding missing mechanism, presence of effect modification or unmeasured confounding. Additionally, we demonstrated how missingness graphs help clarifying the missing structure. When no effect modification existed, complete case analysis yielded valid causal treatment effects even when data were missing not at random. In some situations, complete case analysis was also able to partially correct for unmeasured confounding. Multiple imputation worked well if the data were missing (completely) at random, and if the imputation model was correctly specified. In the presence of effect modification, more complex imputation models than default options of commonly used statistical software were required. Multiple imputation may fail when data are missing not at random. Here, combining multiple imputation and the missing indicator method reduced the bias as the missing indicator variable can be a proxy for unobserved confounding. The optimal way to handle missing values in covariates of propensity score models depends on the missing data structure and the presence of effect modification. When effect modification is present, default settings of imputation methods may yield biased results even if data are missing at random.

Missing responses generally exist in educational and psychological assessments. The statistical inference will lead to serious deviation if the missing responses are not properly modeled in the framework of non-ignorable missing mechanism. In this current study, it is studied whether the different missing mechanism (ignorable missing and non-ignorable missing) models are appropriate to analyze the missing response data from the perspective of parameter estimation and model assessment. In addition, a highly effective Bayesian sampling algorithm based on auxiliary variables is used to estimate the complex models. Compared with the traditional marginal likelihood method and other Bayesian algorithms, the advantages of the new algorithm are discussed in detail. Based on the Markov Chain Monte carlo samples from the posterior distributions, the deviance information criterion (DIC) and the logarithm of the pseudomarignal likelihood (LPML) are employed to compare the different missing mechanism models. Four simulation studies are conducted and a detailed analysis of PISA science data is carried out to further illustrate the proposed methodology.

Incomplete data is a pervasive challenge across a wide range of data types, including tabular, sensor, time-series, image, and textual data. Its presence stems from various real-world factors and gives rise to different missingness mechanisms. While much of the existing research focuses on the Missing Completely At Random (MCAR) assumption, the more complex and realistic mechanisms-Missing At Random (MAR) and Missing Not At Random (MNAR)-remain relatively underexplored despite their prevalence and impact. This PhD project aims to systematically investigate the challenges posed by diverse Incomplete data mechanisms and to develop robust machine learning methods that can perform reliably across MCAR, MAR, and MNAR scenarios. The research spans multiple data modalities and focuses on improving both the theoretical understanding and practical handling of incomplete data. By addressing mechanism-specific imputation challenges and proposing broadly applicable solutions, this work contributes to building more resilient and trustworthy data-driven systems in real-world settings.